AIIMS 2006 Physics Rotational Dynamics Assertion Reason Question

To tackle the question effectively, let's break down both the assertion and reason in detail, and then analyze the options.

Assertion:

A judo fighter in order to throw his opponent on to the mat tries to initially bend his opponent and then rotate him around his hip.

This assertion is true. In judo, the technique often involves bending the opponent to lower their center of gravity and then using rotational movements around the fighter's hip. This technique allows the fighter to utilize leverage effectively, making it easier to lift and throw the opponent.

Reason:

As the mass of the opponent is brought closer to the fighter’s hip, the force required to throw the opponent is reduced.

This reason is also true. The force required to rotate an object (in this case, the opponent) around a pivot point (the fighter's hip) is influenced by the distance of the mass from that pivot. This relationship can be understood through the concept of torque, which is given by the formula:

$$\tau = r \times F$$

where:

• $\tau$ is the torque,
• $r$ is the perpendicular distance from the pivot point to the line of action of the force,
• $F$ is the force applied.

When the opponent's mass is closer to the hip (i.e., the radius $r$ is smaller), the torque required to rotate them decreases. As a result, less force is required to achieve the same rotational effect.

Conclusion on the Correct Answer:

Since both the assertion and the reason are true and the reason correctly explains the assertion, the correct answer is A) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

Explanation of Incorrect Options:

• B) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion: This option is incorrect because the reason provided directly relates to the mechanics of throwing the opponent and correctly explains why bending their mass closer reduces the required force.

• C) Assertion is true but Reason is false: This option is incorrect as both the assertion and reason are true. The reasoning accurately reflects the physics involved in the situation.

• D) Both Assertion and Reason are false: This option is incorrect because both statements are indeed true.

Relevant Concepts:

1. Torque: As explained, torque is a crucial concept in rotational dynamics. The effectiveness of a judo throw relies on the application of torque to rotate the opponent around the fighter's hip.
2. Center of Mass: Bringing the opponent’s center of mass closer to the fighter's hip alters the dynamics of the throw, making it easier to apply the necessary force to complete the action.

In summary, understanding the mechanics of torque and the significance of distance in rotational dynamics helps clarify both the assertion and the reason, reinforcing why option A is the correct choice.